A student measures the activity of a long-lived radioactive source using a Geiger-Müller counter. In a counting time of 5.0 minutes5.0\text{ minutes}5.0 minutes, the counter records 400 counts (corrected for background). Due to the random nature of radioactive decay, there is a statistical uncertainty associated with this count.
By what factor must the counting time be increased so that the percentage uncertainty in the count rate is reduced to exactly one-quarter of its original value?
222
444
888
161616